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In many parts of the United States and the world, there exists large scale innumeracy. From interviewing students placed into developmental skills classes at New York area community colleges, student misconceptions in solving fraction and decimal problems were identified. A much larger group of approximately 500 students were then asked to solve each computational item and also choose strategies they believed were correct. Item Response Theory (IRT) based on logistic modeling allowed for the sample-free calibration of the psychometric characteristics of the items. From a cognitive perspective, the resilts may have implications for the way basic math should be taught.